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Level	Weight	Analytic conductor	$Nk^2$	Dim.

Bad $p$	Char.	Primitive character	Character order	Coefficient field

Self-twists	CM/RM discriminant	Inner twist count	Is self-dual	Analytic rank

Coefficient ring index	Coefficient ring gens.		Projective image	Projective image type
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Results (1-50 of 639 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Coefficient ring index	Sato-Tate	$q$-expansion
164.1.l.a	$164$	$1$	164.l	164.l	$10$	$4$	$1$	$0.082$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$2$	$0$	$1$		$q+\zeta_{10}^{2}q^{2}+\zeta_{10}^{4}q^{4}+(\zeta_{10}-\zeta_{10}^{2}+\cdots)q^{5}+\cdots$
183.1.l.a	$183$	$1$	183.l	183.l	$10$	$4$	$1$	$0.091$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-5$	$1$		$q-\zeta_{10}q^{3}-\zeta_{10}^{2}q^{4}+(-1-\zeta_{10}^{3}+\cdots)q^{7}+\cdots$
264.1.r.a	$264$	$1$	264.r	264.r	$10$	$4$	$1$	$0.132$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$-1$	$1$	$0$	$0$	$1$		$q+\zeta_{10}^{2}q^{2}+\zeta_{10}^{3}q^{3}+\zeta_{10}^{4}q^{4}+\cdots$
264.1.r.b	$264$	$1$	264.r	264.r	$10$	$4$	$1$	$0.132$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$1$	$1$	$0$	$0$	$1$		$q-\zeta_{10}^{2}q^{2}-\zeta_{10}^{4}q^{3}+\zeta_{10}^{4}q^{4}+\cdots$
275.1.s.a	$275$	$1$	275.s	275.s	$10$	$4$	$1$	$0.137$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$0$	$-4$	$0$	$1$		$q+(\zeta_{10}-\zeta_{10}^{3})q^{3}-\zeta_{10}^{2}q^{4}-q^{5}+\cdots$
279.1.v.a	$279$	$1$	279.v	31.f	$10$	$4$	$1$	$0.139$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$-2$	$1$		$q+\zeta_{10}q^{4}+(-\zeta_{10}^{3}+\zeta_{10}^{4})q^{7}+(-\zeta_{10}+\cdots)q^{13}+\cdots$
308.1.s.a	$308$	$1$	308.s	308.s	$10$	$4$	$1$	$0.154$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-1$	$0$	$0$	$1$	$1$		$q+\zeta_{10}^{4}q^{2}-\zeta_{10}^{3}q^{4}-\zeta_{10}^{2}q^{7}+\cdots$
308.1.s.b	$308$	$1$	308.s	308.s	$10$	$4$	$1$	$0.154$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$1$	$0$	$0$	$-1$	$1$		$q+\zeta_{10}^{3}q^{2}-\zeta_{10}q^{4}+\zeta_{10}^{2}q^{7}-\zeta_{10}^{4}q^{8}+\cdots$
328.1.t.a	$328$	$1$	328.t	328.t	$10$	$4$	$1$	$0.164$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$1$	$0$	$0$	$0$	$1$		$q-\zeta_{10}^{2}q^{2}+(\zeta_{10}^{2}+\zeta_{10}^{3})q^{3}+\zeta_{10}^{4}q^{4}+\cdots$
376.1.e.c	$376$	$1$	376.e	376.e	$2$	$4$	$4$	$0.188$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-47}) $	None		$4$	$0$	$-1$	$0$	$0$	$2$	$1$		$q-\zeta_{10}^{3}q^{2}+(-\zeta_{10}-\zeta_{10}^{4})q^{3}-\zeta_{10}q^{4}+\cdots$
395.1.c.c	$395$	$1$	395.c	395.c	$2$	$4$	$4$	$0.197$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-79}) $	None		$4$	$0$	$0$	$0$	$-1$	$0$	$1$		$q+(\zeta_{10}+\zeta_{10}^{4})q^{2}+(-1+\zeta_{10}^{2}-\zeta_{10}^{3}+\cdots)q^{4}+\cdots$
400.1.x.a	$400$	$1$	400.x	100.h	$10$	$4$	$1$	$0.200$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$1$	$0$	$1$		$q+\zeta_{10}^{3}q^{5}-\zeta_{10}^{4}q^{9}+(\zeta_{10}+\zeta_{10}^{2}+\cdots)q^{13}+\cdots$
429.1.v.c	$429$	$1$	429.v	429.v	$10$	$8$	$2$	$0.214$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-39}) $	None		$8$	$0$	$0$	$2$	$0$	$0$	$1$		$q+(-\zeta_{20}+\zeta_{20}^{5})q^{2}-\zeta_{20}^{4}q^{3}+(-1+\cdots)q^{4}+\cdots$
475.1.m.a	$475$	$1$	475.m	475.m	$10$	$4$	$1$	$0.237$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$-1$	$0$	$1$		$q+\zeta_{10}^{3}q^{4}-\zeta_{10}q^{5}+(\zeta_{10}+\zeta_{10}^{4}+\cdots)q^{7}+\cdots$
539.1.l.a	$539$	$1$	539.l	11.d	$10$	$4$	$1$	$0.269$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{10}+\zeta_{10}^{3})q^{2}+(-\zeta_{10}+\zeta_{10}^{2}+\cdots)q^{4}+\cdots$
539.1.t.a	$539$	$1$	539.t	77.o	$30$	$8$	$1$	$0.269$	$\Q(\zeta_{15})$	$D_{10}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{30}^{4}-\zeta_{30}^{13})q^{2}+(-\zeta_{30}^{2}+\cdots)q^{4}+\cdots$
543.1.m.a	$543$	$1$	543.m	543.m	$10$	$4$	$1$	$0.271$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$0$	$1$		$q-\zeta_{10}^{4}q^{3}+\zeta_{10}^{3}q^{4}+(\zeta_{10}^{2}+\zeta_{10}^{3}+\cdots)q^{7}+\cdots$
564.1.f.c	$564$	$1$	564.f	564.f	$2$	$4$	$4$	$0.281$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-47}) $	None		$4$	$0$	$-1$	$1$	$0$	$0$	$1$		$q-\zeta_{10}^{3}q^{2}+\zeta_{10}q^{3}-\zeta_{10}q^{4}-\zeta_{10}^{4}q^{6}+\cdots$
564.1.f.d	$564$	$1$	564.f	564.f	$2$	$4$	$4$	$0.281$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-47}) $	None		$4$	$0$	$1$	$-1$	$0$	$0$	$1$		$q+\zeta_{10}q^{2}-\zeta_{10}^{3}q^{3}+\zeta_{10}^{2}q^{4}-\zeta_{10}^{4}q^{6}+\cdots$
595.1.b.b	$595$	$1$	595.b	595.b	$2$	$8$	$8$	$0.297$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-119}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{20}^{2}+\zeta_{20}^{8})q^{2}+(-\zeta_{20}^{3}-\zeta_{20}^{7}+\cdots)q^{3}+\cdots$
600.1.z.a	$600$	$1$	600.z	600.z	$10$	$8$	$2$	$0.299$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-6}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{20}q^{2}+\zeta_{20}^{7}q^{3}+\zeta_{20}^{2}q^{4}+\zeta_{20}q^{5}+\cdots$
616.1.bh.a	$616$	$1$	616.bh	616.ah	$10$	$4$	$1$	$0.307$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$1$	$0$	$0$	$1$	$1$		$q-\zeta_{10}^{4}q^{2}-\zeta_{10}^{3}q^{4}-\zeta_{10}^{2}q^{7}+\cdots$
616.1.bh.b	$616$	$1$	616.bh	616.ah	$10$	$4$	$1$	$0.307$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$1$	$0$	$0$	$1$	$1$		$q+\zeta_{10}^{3}q^{2}-\zeta_{10}q^{4}-\zeta_{10}^{2}q^{7}-\zeta_{10}^{4}q^{8}+\cdots$
616.1.bq.a	$616$	$1$	616.bq	616.aq	$10$	$4$	$1$	$0.307$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-1$	$0$	$0$	$1$	$1$		$q-\zeta_{10}^{3}q^{2}-\zeta_{10}q^{4}-\zeta_{10}^{2}q^{7}+\zeta_{10}^{4}q^{8}+\cdots$
616.1.bq.b	$616$	$1$	616.bq	616.aq	$10$	$4$	$1$	$0.307$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$1$	$0$	$0$	$-1$	$1$		$q-\zeta_{10}^{4}q^{2}-\zeta_{10}^{3}q^{4}+\zeta_{10}^{2}q^{7}+\cdots$
632.1.f.c	$632$	$1$	632.f	632.f	$2$	$4$	$4$	$0.315$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-79}) $	None		$4$	$0$	$-1$	$0$	$0$	$0$	$1$		$q-\zeta_{10}^{3}q^{2}-\zeta_{10}q^{4}+(-\zeta_{10}-\zeta_{10}^{4}+\cdots)q^{5}+\cdots$
651.1.bu.a	$651$	$1$	651.bu	651.au	$10$	$4$	$1$	$0.325$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$1$	$1$		$q-\zeta_{10}q^{3}-\zeta_{10}^{3}q^{4}-\zeta_{10}^{4}q^{7}+\zeta_{10}^{2}q^{9}+\cdots$
651.1.bu.b	$651$	$1$	651.bu	651.au	$10$	$4$	$1$	$0.325$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$1$	$1$		$q+\zeta_{10}q^{3}-\zeta_{10}^{3}q^{4}-\zeta_{10}^{2}q^{7}+\zeta_{10}^{2}q^{9}+\cdots$
655.1.d.e	$655$	$1$	655.d	655.d	$2$	$4$	$4$	$0.327$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-131}) $	None		$4$	$0$	$0$	$0$	$1$	$0$	$1$		$q+(\zeta_{10}+\zeta_{10}^{4})q^{3}-q^{4}-\zeta_{10}^{2}q^{5}+\cdots$
693.1.br.b	$693$	$1$	693.br	77.j	$10$	$8$	$2$	$0.346$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$0$	$0$	$0$	$2$	$1$		$q+(-\zeta_{20}^{3}-\zeta_{20}^{9})q^{2}+(-\zeta_{20}^{2}+\zeta_{20}^{6}+\cdots)q^{4}+\cdots$
704.1.x.a	$704$	$1$	704.x	88.p	$10$	$8$	$2$	$0.351$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-2}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{20}^{7}-\zeta_{20}^{9})q^{3}+(-\zeta_{20}^{4}+\zeta_{20}^{6}+\cdots)q^{9}+\cdots$
711.1.d.c	$711$	$1$	711.d	79.b	$2$	$4$	$4$	$0.355$	$\Q(\zeta_{20})^+$	$D_{10}$	$\Q(\sqrt{-79}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+\beta _{3}q^{5}+(-\beta _{1}+\cdots)q^{8}+\cdots$
723.1.o.a	$723$	$1$	723.o	723.o	$10$	$4$	$1$	$0.361$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$0$	$1$		$q+\zeta_{10}q^{3}+q^{4}+(-\zeta_{10}^{2}+\zeta_{10}^{4}+\cdots)q^{7}+\cdots$
748.1.s.c	$748$	$1$	748.s	748.s	$10$	$8$	$2$	$0.373$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-17}) $	None		$8$	$0$	$2$	$0$	$0$	$0$	$1$		$q+\zeta_{20}^{6}q^{2}+(-\zeta_{20}+\zeta_{20}^{5})q^{3}-\zeta_{20}^{2}q^{4}+\cdots$
775.1.z.a	$775$	$1$	775.z	775.z	$10$	$4$	$1$	$0.387$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$-5$	$0$	$1$	$0$	$1$		$q+(-1+\zeta_{10}^{4})q^{2}+(1-\zeta_{10}^{3}-\zeta_{10}^{4}+\cdots)q^{4}+\cdots$
776.1.h.d	$776$	$1$	776.h	776.h	$2$	$4$	$4$	$0.387$	$\Q(\zeta_{20})^+$	$D_{10}$	$\Q(\sqrt{-194}) $	None	✓	$4$	$0$	$-4$	$-2$	$0$	$0$	$1$		$q-q^{2}+\beta _{2}q^{3}+q^{4}-\beta _{1}q^{5}-\beta _{2}q^{6}+\cdots$
792.1.bs.a	$792$	$1$	792.bs	88.p	$10$	$4$	$1$	$0.395$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-6}) $	None		$4$	$0$	$-1$	$0$	$0$	$0$	$1$		$q-\zeta_{10}^{3}q^{2}-\zeta_{10}q^{4}+(-\zeta_{10}+\zeta_{10}^{3}+\cdots)q^{5}+\cdots$
792.1.bs.b	$792$	$1$	792.bs	88.p	$10$	$4$	$1$	$0.395$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-6}) $	None		$4$	$0$	$1$	$0$	$0$	$0$	$1$		$q+\zeta_{10}^{3}q^{2}-\zeta_{10}q^{4}+(\zeta_{10}-\zeta_{10}^{3}+\cdots)q^{5}+\cdots$
795.1.b.b	$795$	$1$	795.b	795.b	$2$	$8$	$8$	$0.397$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-159}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{20}^{3}+\zeta_{20}^{7})q^{2}-\zeta_{20}^{5}q^{3}+(-1+\cdots)q^{4}+\cdots$
799.1.c.d	$799$	$1$	799.c	799.c	$2$	$4$	$4$	$0.399$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-47}) $	None		$4$	$0$	$2$	$0$	$0$	$0$	$1$		$q+(-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+(\zeta_{10}+\zeta_{10}^{4}+\cdots)q^{3}+\cdots$
820.1.bd.a	$820$	$1$	820.bd	820.ad	$10$	$4$	$1$	$0.409$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$-1$	$0$	$1$	$0$	$1$		$q+\zeta_{10}^{2}q^{2}+(-\zeta_{10}-\zeta_{10}^{4})q^{3}+\zeta_{10}^{4}q^{4}+\cdots$
820.1.bd.b	$820$	$1$	820.bd	820.ad	$10$	$4$	$1$	$0.409$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$1$	$0$	$1$	$0$	$1$		$q-\zeta_{10}^{2}q^{2}+(\zeta_{10}+\zeta_{10}^{4})q^{3}+\zeta_{10}^{4}q^{4}+\cdots$
824.1.h.d	$824$	$1$	824.h	824.h	$2$	$4$	$4$	$0.411$	$\Q(\zeta_{20})^+$	$D_{10}$	$\Q(\sqrt{-206}) $	None	✓	$4$	$0$	$-4$	$0$	$0$	$-2$	$1$		$q-q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{3}q^{5}+\beta _{1}q^{6}+\cdots$
824.1.h.e	$824$	$1$	824.h	824.h	$2$	$4$	$4$	$0.411$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-103}) $	None		$4$	$0$	$1$	$0$	$0$	$-2$	$1$		$q+\zeta_{10}q^{2}+\zeta_{10}^{2}q^{4}+(\zeta_{10}^{2}-\zeta_{10}^{3}+\cdots)q^{7}+\cdots$
852.1.o.a	$852$	$1$	852.o	852.o	$10$	$4$	$1$	$0.425$	$\Q(\zeta_{10})$	$D_{10}$	None	$\Q(\sqrt{3}) $		$4$	$0$	$-1$	$1$	$0$	$0$	$1$		$q+\zeta_{10}^{2}q^{2}-\zeta_{10}^{2}q^{3}+\zeta_{10}^{4}q^{4}+\cdots$
852.1.o.b	$852$	$1$	852.o	852.o	$10$	$4$	$1$	$0.425$	$\Q(\zeta_{10})$	$D_{10}$	None	$\Q(\sqrt{3}) $		$4$	$0$	$1$	$-1$	$0$	$0$	$1$		$q-\zeta_{10}^{2}q^{2}+\zeta_{10}^{2}q^{3}+\zeta_{10}^{4}q^{4}+\cdots$
895.1.d.c	$895$	$1$	895.d	895.d	$2$	$4$	$4$	$0.447$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-179}) $	None		$4$	$0$	$0$	$0$	$-1$	$0$	$1$		$q+(\zeta_{10}+\zeta_{10}^{4})q^{3}-q^{4}-\zeta_{10}^{3}q^{5}+\cdots$
900.1.bb.a	$900$	$1$	900.bb	100.h	$10$	$8$	$2$	$0.449$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-1}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{20}^{3}q^{2}+\zeta_{20}^{6}q^{4}+\zeta_{20}^{9}q^{5}+\cdots$
915.1.bh.a	$915$	$1$	915.bh	915.ah	$10$	$4$	$1$	$0.457$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$0$	$-1$	$1$	$0$	$1$		$q+(\zeta_{10}^{3}+\zeta_{10}^{4})q^{2}-\zeta_{10}q^{3}+(-\zeta_{10}+\cdots)q^{4}+\cdots$
915.1.bh.b	$915$	$1$	915.bh	915.ah	$10$	$4$	$1$	$0.457$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$0$	$1$	$-1$	$0$	$1$		$q+(-\zeta_{10}^{3}-\zeta_{10}^{4})q^{2}+\zeta_{10}q^{3}+(-\zeta_{10}+\cdots)q^{4}+\cdots$

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.